DOCSLIB.ORG

Chapter 6 Thermodynamics and the Equations of Motion

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Chapter 6 Thermodynamics and the Equations of Motion Chapter 6 Thermodynamics and the Equations of Motion 6.1 The first law of thermodynamics for a fluid and the equation of state. We noted in chapter 4 that the full formulation of the equations of motion required additional information to deal with the state variables density and pressure and that we were one equation short of matching unknowns and equations. In both meteorology and oceanography the variation of density and hence buoyancy is critical in many phenomenon such cyclogenesis and the thermohaline circulation, to name only two. To close the system we will have to include the thermodynamics pertinent to the fluid motion. In this course we will examine a swift review of those basic facts from thermodynamics we will need to complete our dynamical formulation. In actuality, thermodynamics is a misnomer. Classical thermodynamics deals with equilibrium states in which there are no variations of the material in space or time, hardly the situation of interest to us. However, we assume that we can subdivide the fluid into regions small enough to allow the continuum field approximation but large enough, and changing slowly enough so that locally thermodynamic equilibrium is established allowing a reasonable definition of thermodynamic state variables like pressure, density and pressure. We have already noted that for some quantities, like the pressure for molecules with more than translational degrees of freedom, the departures from thermodynamic equilibrium have to be considered. Generally, such considerations are of minor importance in the fluid mechanics of interest to us. If the fluid is in thermodynamic equilibrium any thermodynamic variable for a pure substance, like pure water, can be written in terms of any two other thermodynamic variables✿, i.e. p = p(!,T ) (6.1.1) where the functional relationship in depends on the substance. Note that, as discussed before, (6.1.11) does not necessarily yield a pressure that is the average normal force on a fluid element. The classic example of an equation of state is the perfect gas law; p = !RT (6.1.2) which is appropriate for dry air. The constant R is the gas constant and is a property of the material that must be specified. For air (from Batchelor) R = 2.870x103cm2 / sec2 degC (6.1.3) One of the central results of thermodynamics is the specification of another thermodynamic state variable e(ρ,T) which is the internal energy per unit mass and is, in fact, defined by a statement of the first law of thermodynamics. Consider a fluid volume, V, of fixed mass (Figure 6.1.1) dA ! n ij j V Kj ✿ For sea water, the presence of salt renders the equation of state very complex. There are tomes written on the subject and we will slide over this issue entirely in Chapter 6 2 Fi Figure 6.1.1 A fixed mass of fluid, of volume V, subject to body force F, a surface flux of heat (per unit surface area) out of the volume, K, and the surface force per unit area due to the surface stress tensor. The first law of thermodynamics states that the rate of change of the total energy of the fixed mass of fluid in V, i.e. the rate of change of the sum of the kinetic energy and internal energy is equal to the rate of work done on the fluid mass plus the rate at which heat added to the fluid mass. That is, b " a #%$%&% !c #$d & e !f d ! 2 " ! " $ " ' " ( !e + ! u / 2 dV = ( !FiudV + ( ui) ijn j dA + ( !Q dV * ( Kinˆ dA (6.1.4) dt V $ ' V A V A # & Let’s discuss each term : (a) The rate of change of internal energy. (b) The rate of change of kinetic energy. (c) The rate at which the body force does work. This is the scalar product of the body force with the fluid velocity. (d) The rate at which the surface force does work. This is the scalar product of the surface stress with the velocity at the surface (then integrated over the surface). (e) The rate at which heat per unit mass is added to the fluid. Here Q is the thermodynamic equivalent of the body force, i.e. the heat added per unit mass. this course. Chapter 6 3 ! (f) K is the heat flux vector at the surface, i.e. the rate of heat flow per unit surface area out of the volume. The terms (a) and (b) require little discussion. They are the internal and kinetic energies rates of change for the fixed mass enclosed in V. Note that term (b) is: d uiui dui " ! dV = " !ui dV (6.1.5) dt V 2 V dt The principal point to make here is that (6.1.4) defines the internal energy as the term needed to balance the energy budget. What thermodynamic theory shows is that e is a state variable defined by pressure and temperature, for example, and independent of the process that has led to the state described by those variables. Similarly, term (c) is the rate at which the body force does work. The work is the force multiplied by the distance moved in the direction of the force. The work per unit time is the force multiplied by the velocity in the direction of the force and then, of course, integrated over the mass of the body. Term (d) is the surface force at some element of surface enclosing V and is multiplied by the velocity at that point on the surface and then integrated over the surface. Using the divergence theorem, #ui! ij #! ij #ui " ui! ijn jdA = " dV = " ui dV + " ! ij dV (6.1.6) A V #x j V #x j V #x j Term (e) represents the rate of heat addition by heat sources that are proportional to the volume of the fluid, for example, the release of latent heat in the atmosphere or geothermal heating in the ocean or penetrative solar radiation in the ocean and atmosphere. Finally the flux of heat out of the system in term (f) can also be written in terms of a volume integral, ! "K j ! KinˆdA = ! dV (6.1.7) A V "x j Chapter 6 4 Now that all terms in the budget are written a volume integrals we can group them is a useful way as, % dui #$ ij ( de #ui #K j + ui '! " !Fi " *dV + + ! dV = + $ ij dV + + !QdV " + dV (6.1 V &' dt #x j )* V dt V #x j V V #x j .8) The first term on the left hand side has an integrand which is (nearly) the momentum equation if Fi contains all the body forces including the centrifugal force. It lacks only the Coriolis acceleration. However, since each term is dotted with the velocity one could easily add the Coriolis acceleration to the bracket without changing the result. Then it is clear that the whole first term adds to zero and is, in fact, just a statement of the budget of kinetic energy 2 dui / 2 "# ij ! = !ui Fi + ui (6.1.9) dt "x j The remaining volume integral must then vanish and using, as before, the fact that the chosen volume is arbitrary means its integrand must vanish or, de #ui #K j ! = " ij + !Q $ (6.1.10) dt #x j #x j as the governing equation for the internal energy alone. Since the stress tensor is symmetric, "ui "u j "u j ! ij = ! ji = ! ij "x j "xi "xi (6.1.11) 1 # "ui "u j & = ! ij % + ( = ! ijeij 2 $ "x j "xi ' Chapter 6 5 The first step in (6.1.11) is just a relabeled form with i and j interchanged. The second step uses the symmetry of the stress tensor and the last line rewrites the result in terms of the inner product of the stress tensor and the rate of strain tensor. Since, (3.7.15) ! ij = " p#ij + 2µeij + $ekk#ij (6.1.12) 2 or with the relation , ! = " # 3µ we have 1 ! = " p# + 2µ(e " e # ) + $e # (6.1.13) ij ij ij 3 kk ij kk ij where the pressure is the thermodynamic pressure of the equation of state and η is the coefficient relating to the deviation of that pressure from the average normal stress on a fluid element. The scalar ! $ 2 1 2 ' 2 ! ijeij = " p#iu + 2µ eij " ekk + *ekk (6.1.14) %& 3 () " 2 1 2 % The term eij ! ekk can be shown to be always positive (it’s is easiest to do this #$ 3 &' in a coordinate system where the rate of strain tensor is diagonalized). So this term always represents an increase of internal energy provided by the viscous dissipation of mechanical energy. Traditionally, this term is defined as the dissipation function, Φ , i.e. where, µ $ 2 1 2 ' ! = 2 eij # ekk (6.1.15) " %& 3 () In much the same way that we approached the relation between the stress tensor and the velocity gradients, we assume that the heat flux vector depends linearly on the local value of the temperature gradient, or, in the general case Chapter 6 6 "T Ki = !ij (6.1.16) "x j Again assuming that the medium is isotropic in terms of the relation between temperature gradient and heat flux, the tensor !ij needs to be a second order isotropic tensor. The only such tensor is the kronecker delta so %T !ij = "k#ij $ Ki = "k , %xi (6.1.17) The minus sign in (6.1.17) expresses our knowledge that heat flows from hot to cold, i.e. down the temperature gradient, i.e.
Load more

Recommended publications
  • Thermodynamics Notes
    Thermodynamics Notes Steven K. Krueger Department of Atmospheric Sciences, University of Utah August 2020 Contents 1 Introduction 1 1.1 What is thermodynamics? . .1 1.2 The atmosphere . .1 2 The Equation of State 1 2.1 State variables . .1 2.2 Charles' Law and absolute temperature . .2 2.3 Boyle's Law . .3 2.4 Equation of state of an ideal gas . .3 2.5 Mixtures of gases . .4 2.6 Ideal gas law: molecular viewpoint . .6 3 Conservation of Energy 8 3.1 Conservation of energy in mechanics . .8 3.2 Conservation of energy: A system of point masses . .8 3.3 Kinetic energy exchange in molecular collisions . .9 3.4 Working and Heating . .9 4 The Principles of Thermodynamics 11 4.1 Conservation of energy and the first law of thermodynamics . 11 4.1.1 Conservation of energy . 11 4.1.2 The first law of thermodynamics . 11 4.1.3 Work . 12 4.1.4 Energy transferred by heating . 13 4.2 Quantity of energy transferred by heating . 14 4.3 The first law of thermodynamics for an ideal gas . 15 4.4 Applications of the first law . 16 4.4.1 Isothermal process . 16 4.4.2 Isobaric process . 17 4.4.3 Isosteric process . 18 4.5 Adiabatic processes . 18 5 The Thermodynamics of Water Vapor and Moist Air 21 5.1 Thermal properties of water substance . 21 5.2 Equation of state of moist air . 21 5.3 Mixing ratio . 22 5.4 Moisture variables . 22 5.5 Changes of phase and latent heats .
    [Show full text]
  • Thermodynamics
    ME346A Introduction to Statistical Mechanics { Wei Cai { Stanford University { Win 2011 Handout 6. Thermodynamics January 26, 2011 Contents 1 Laws of thermodynamics 2 1.1 The zeroth law . .3 1.2 The first law . .4 1.3 The second law . .5 1.3.1 Efficiency of Carnot engine . .5 1.3.2 Alternative statements of the second law . .7 1.4 The third law . .8 2 Mathematics of thermodynamics 9 2.1 Equation of state . .9 2.2 Gibbs-Duhem relation . 11 2.2.1 Homogeneous function . 11 2.2.2 Virial theorem / Euler theorem . 12 2.3 Maxwell relations . 13 2.4 Legendre transform . 15 2.5 Thermodynamic potentials . 16 3 Worked examples 21 3.1 Thermodynamic potentials and Maxwell's relation . 21 3.2 Properties of ideal gas . 24 3.3 Gas expansion . 28 4 Irreversible processes 32 4.1 Entropy and irreversibility . 32 4.2 Variational statement of second law . 32 1 In the 1st lecture, we will discuss the concepts of thermodynamics, namely its 4 laws. The most important concepts are the second law and the notion of Entropy. (reading assignment: Reif x 3.10, 3.11) In the 2nd lecture, We will discuss the mathematics of thermodynamics, i.e. the machinery to make quantitative predictions. We will deal with partial derivatives and Legendre transforms. (reading assignment: Reif x 4.1-4.7, 5.1-5.12) 1 Laws of thermodynamics Thermodynamics is a branch of science connected with the nature of heat and its conver- sion to mechanical, electrical and chemical energy. (The Webster pocket dictionary defines, Thermodynamics: physics of heat.) Historically, it grew out of efforts to construct more efficient heat engines | devices for ex- tracting useful work from expanding hot gases (http://www.answers.com/thermodynamics).
    [Show full text]
  • Chapter03 Introduction to Thermodynamic Systems
    Chapter03 Introduction to Thermodynamic Systems February 13, 2019 This chapter introduces the concept of thermo- Remark 1.1. In general, we will consider three kinds dynamic systems and digresses on the issue: How of exchange between S and Se through a (possibly ab- complex systems are related to Statistical Thermo- stract) membrane: dynamics. To do so, let us review the concepts of (1) Diathermal (Contrary: Adiabatic) membrane Equilibrium Thermodynamics from the conventional that allows exchange of thermal energy. viewpoint. Let U be the universe. Let a collection of objects (2) Deformable (Contrary: Rigid) membrane that S ⊆ U be defined as the system under certain restric- allows exchange of work done by volume forces tive conditions. The complement of S in U is called or surface forces. the exterior of S and is denoted as Se. (3) Permeable (Contrary: Impermeable) membrane that allows exchange of matter (e.g., in the form 1 Basic Definitions of molecules of chemical species). Definition 1.1. A system S is an idealized body that can be isolated from Se in the sense that changes in Se Definition 1.4. A thermodynamic state variable is a do not have any effects on S. macroscopic entity that is a characteristic of a system S. A thermodynamic state variable can be a scalar, Definition 1.2. A system S is called a thermody- a finite-dimensional vector, or a tensor. Examples: namic system if any possible exchange between S and temperature, or a strain tensor. Se is restricted to one or more of the following: (1) Any form of energy (e.g., thermal, electric, and magnetic) Definition 1.5.
    [Show full text]
  • Statistical Thermodynamics - Fall 2009
    1 Statistical Thermodynamics - Fall 2009 Professor Dmitry Garanin Thermodynamics September 9, 2012 I. PREFACE The course of Statistical Thermodynamics consist of two parts: Thermodynamics and Statistical Physics. These both branches of physics deal with systems of a large number of particles (atoms, molecules, etc.) at equilibrium. 3 19 One cm of an ideal gas under normal conditions contains NL =2.69 10 atoms, the so-called Loschmidt number. Although one may describe the motion of the atoms with the help of× Newton’s equations, direct solution of such a large number of differential equations is impossible. On the other hand, one does not need the too detailed information about the motion of the individual particles, the microscopic behavior of the system. One is rather interested in the macroscopic quantities, such as the pressure P . Pressure in gases is due to the bombardment of the walls of the container by the flying atoms of the contained gas. It does not exist if there are only a few gas molecules. Macroscopic quantities such as pressure arise only in systems of a large number of particles. Both thermodynamics and statistical physics study macroscopic quantities and relations between them. Some macroscopics quantities, such as temperature and entropy, are non-mechanical. Equilibruim, or thermodynamic equilibrium, is the state of the system that is achieved after some time after time-dependent forces acting on the system have been switched off. One can say that the system approaches the equilibrium, if undisturbed. Again, thermodynamic equilibrium arises solely in macroscopic systems. There is no thermodynamic equilibrium in a system of a few particles that are moving according to the Newton’s law.
    [Show full text]
  • Lecture 6: Entropy
    Matthew Schwartz Statistical Mechanics, Spring 2019 Lecture 6: Entropy 1 Introduction In this lecture, we discuss many ways to think about entropy. The most important and most famous property of entropy is that it never decreases Stot > 0 (1) Here, Stot means the change in entropy of a system plus the change in entropy of the surroundings. This is the second law of thermodynamics that we met in the previous lecture. There's a great quote from Sir Arthur Eddington from 1927 summarizing the importance of the second law: If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equationsthen so much the worse for Maxwell's equations. If it is found to be contradicted by observationwell these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of ther- modynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. Another possibly relevant quote, from the introduction to the statistical mechanics book by David Goodstein: Ludwig Boltzmann who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. There are many ways to dene entropy. All of them are equivalent, although it can be hard to see. In this lecture we will compare and contrast dierent denitions, building up intuition for how to think about entropy in dierent contexts. The original denition of entropy, due to Clausius, was thermodynamic.
    [Show full text]
  • Session 15 Thermodynamics
    Session 15 Thermodynamics Cheryl Hurkett Physics Innovations Centre for Excellence in Learning and Teaching CETL (Leicester) Department of Physics and Astronomy University of Leicester 1 Contents Welcome .................................................................................................................................. 4 Session Authors .................................................................................................................. 4 Learning Objectives .............................................................................................................. 5 The Problem ........................................................................................................................... 6 Issues .................................................................................................................................... 6 Energy, Heat and Work ........................................................................................................ 7 The First Law of thermodynamics................................................................................... 8 Work..................................................................................................................................... 9 Heat .................................................................................................................................... 11 Principal Specific heats of a gas ..................................................................................... 12 Summary ..........................................................................................................................
    [Show full text]
  • Process and State Variables (PSV)
    Process and State Variables (PSV) Process and State Variables Describing and analyzing processes requires that you can understand, calculate, and manipulate both process data as well as state variables. How would you calculate process variable values from measurements ? • Manipulate process flow data # Interconvert mass, volume, and moles(and their flows) # Calculate mass(mole) fractions from mole(mass) fractions for a mixture • Calculate pressures using a manometer(and explain the concept of gauge pressure) • Interconvert between different temperature scales • Explain the difference between intensive and extensive variables Certain calculations require you to know quite a bit about the "state" of a material(i.e., its state of aggregation(phase), temperature, pressure, chemical composition, etc.).How can we quantify properties about a material 's state? • Calculate State Variables and # Define "state variable" # Explain why one must choose a reference point when calculating state variables # Generate "fictitious paths" from your reference state to your desired state # Use heat capacities and phase data to calculate and from fictitious paths • Use tabular data to determine and PSV: Interconvert mass, volume, and moles (and their flows) Mass and Flow Variables In ChE processes there are a number of variables that typically play an important role. Let's review what some of them are. DEFINITION: Density is the mass of a material per unit volume (specific volume is inverse - i.e., volume per unit mass). DEFINITION: Specific Gravity is the ratio of one material's density to that of a reference material (typically water at 4C). S.G. is dimensionless -> density A/density Ref. Material moves in/out of process units -> flow rate! DEFINITION: The flow rate represents the amount of material that moves into (or out of) a process unit per unit time.
    [Show full text]
  • Calorimetry of 4-Aminopyridine Alan Everett Av N Til Iowa State University
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1976 Calorimetry of 4-aminopyridine Alan Everett aV n Til Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Analytical Chemistry Commons Recommended Citation Van Til, Alan Everett, "Calorimetry of 4-aminopyridine " (1976). Retrospective Theses and Dissertations. 6229. https://lib.dr.iastate.edu/rtd/6229 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This material was produced from a microfilm copy of the original document. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1.The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting thru an image and duplicating adjacent pages to insure you complete continuity. 2. When an image on the film is obliterated with a large round black mark, it is an indication that the photographer suspected that the copy may have moved during exposure and thus cause a blurred image.
    [Show full text]
  • An Equation of State for Insect Swarms Michael Sinhuber1,3,4, Kasper Van Der Vaart1,4, Yenchia Feng1, Andrew M
    www.nature.com/scientificreports OPEN An equation of state for insect swarms Michael Sinhuber1,3,4, Kasper van der Vaart1,4, Yenchia Feng1, Andrew M. Reynolds2 & Nicholas T. Ouellette1* Collective behaviour in focks, crowds, and swarms occurs throughout the biological world. Animal groups are generally assumed to be evolutionarily adapted to robustly achieve particular functions, so there is widespread interest in exploiting collective behaviour for bio-inspired engineering. However, this requires understanding the precise properties and function of groups, which remains a challenge. Here, we demonstrate that collective groups can be described in a thermodynamic framework. We defne an appropriate set of state variables and extract an equation of state for laboratory midge swarms. We then drive swarms through “thermodynamic” cycles via external stimuli, and show that our equation of state holds throughout. Our fndings demonstrate a new way of precisely quantifying the nature of collective groups and provide a cornerstone for potential future engineering design. Organisms on every size scale, from single-celled1 to highly complex2, regularly come together in groups. In many cases, such aggregations are collective, in that the group as a whole displays properties and functionality distinct from those of its individual members or simply their linear sum3,4. It is generally assumed that since evolution has led so many diferent kinds of animals to behave collectively, the performance of collective groups at whatever task they seek to achieve ought to be well beyond the capabilities of a single individual5, while also being robust to uncertain natural environments 6,7 and operating without the need for top-down control 8.
    [Show full text]
  • Specific Heat • Phase Change
    Lecture 16 • Temperature change: specific heat • Phase change: heat of transformation • Calorimetry: calculating heat exchanges • Specific heats of gases • adiabatic processes Thermal properties of matter (I) Joule: heat and work are energy transferred; change in thermal energy change in temperature or phase • Temperature change and Specific Heat specific heat, c = energy to raise T of 1 kg by 1 K (“thermal inertia”) ∆Eth = Mc∆T (temperature change) ∆E = W + Q for solids/liquids, W =0 th ⇒ Molar specific heat, C: Q = nC∆T M(in g) 1000(g/kg) Using n = M = M(in kg): mol Mmol(in g/mol) Mmol(in g/mol) C(in J/mol/K) = c(in J/kg/K) 1000(g/kg) Thermal properties of matter (II) • Phase change and heat of transformation, L T same, heat transferred breaks bonds (instead of speeding up atoms) 1 = Mc L = heat energy for 1 kg to change phase Lf, v: heat of fusion (solid/liquid) or vaporization (liquid/gas) Lv >Lf : bonds not completely broken during melting... Calorimetry • 2 systems interacting thermally, but isolated from others start at T = T , 1 ! 2 heat transferred till equilibrium Tf (Q1 is energy transferred to system 1: > 0 if energy enters...) • Strategy for (> 2 systems) Qnet = Q1 + Q2 + .... =0 Systems with temperature change: Q = Mc(Tf Ti) Q>0 if Tf >Ti Systems with− phase⇒ change: Q + MLf or v: for melting/freezing... ± (check: Tf not higher/lower than all Ti) Specific Heats of Gases • same ∆ T , different Q since W different... • Two versions of molar specific heat (if p or V not constant, use Q = W ∆ E th ) − Relation between CP and CV • ∆
    [Show full text]
  • Lecture 2: Reversibility and Work September 20, 2018 1 / 18 Some More Definitions?
    ...Thermodynamics Equilibrium implies the existence of a thermodynamic quantity Mechanical equilibrium implies Pressure Thermal Equilibrium implies Temperature Zeroth LAW of thermodynamics: There exists a single quantity which determines thermal equilibrium Named by RH Fowler, great great grandsupervisor to Prof Ackland Graeme Ackland Lecture 2: Reversibility and Work September 20, 2018 1 / 18 Some more definitions? Process: when the state variables change in time. Reversible Process: when every step for the system and its surroundings can be reversed. A reversible process involves a series of equilibrium states. Irreversible Process - when the direction of the arrow of time is important. IRREVERSIBILITY DEFINES THE CONCEPT OF TIME. Graeme Ackland Lecture 2: Reversibility and Work September 20, 2018 2 / 18 Reversible processes Reversible processes are quasistatic - system is in equilibrium and the trajectory can be drawn on a PV indicator diagram. Irreversible processes procede via non-equilibrium states, with gradients of T and P, where the system would continue to change if the external driving force is removed (e.g. stirring) It is possible to get between two states of a system by reversible OR irreversible process. The final state of the system is the same regardless of reversibility, but the surroundings are different. Graeme Ackland Lecture 2: Reversibility and Work September 20, 2018 3 / 18 How to tell if a process is reversible Consider a process between equilibrium endpoints (starting point and finishing point) eg compression of gas by a piston from state (P1,V1) to (P2, V2). For a reversible process, every (infinitesimal) step { for both the system and its surroundings { can be reversed.
    [Show full text]
  • Thermodynamics.Pdf
    1 Statistical Thermodynamics Professor Dmitry Garanin Thermodynamics February 24, 2021 I. PREFACE The course of Statistical Thermodynamics consist of two parts: Thermodynamics and Statistical Physics. These both branches of physics deal with systems of a large number of particles (atoms, molecules, etc.) at equilibrium. 3 19 One cm of an ideal gas under normal conditions contains NL = 2:69×10 atoms, the so-called Loschmidt number. Although one may describe the motion of the atoms with the help of Newton's equations, direct solution of such a large number of differential equations is impossible. On the other hand, one does not need the too detailed information about the motion of the individual particles, the microscopic behavior of the system. One is rather interested in the macroscopic quantities, such as the pressure P . Pressure in gases is due to the bombardment of the walls of the container by the flying atoms of the contained gas. It does not exist if there are only a few gas molecules. Macroscopic quantities such as pressure arise only in systems of a large number of particles. Both thermodynamics and statistical physics study macroscopic quantities and relations between them. Some macroscopics quantities, such as temperature and entropy, are non-mechanical. Equilibruim, or thermodynamic equilibrium, is the state of the system that is achieved after some time after time-dependent forces acting on the system have been switched off. One can say that the system approaches the equilibrium, if undisturbed. Again, thermodynamic equilibrium arises solely in macroscopic systems. There is no thermodynamic equilibrium in a system of a few particles that are moving according to the Newton's law.
    [Show full text]